You're on the right way, but there are some more changes necessary.

1. Change the limit (line ~47)
from
$result = sql_query("select sid, title from ${prefix}_stories where (time LIKE '%$tdate%') AND `time` <= now() $querylang order by counter DESC limit 0,1");
to
$result = sql_query("select sid, title from ${prefix}_stories where (time LIKE '%$tdate%') AND `time` <= now() $querylang order by counter DESC limit 0,5");
In my opinion, that's what you've done already.

2. Add this code
while (list($fsid, $ftitle) = sql_fetch_row($result));
$content .= '<br><a href="modules.php?name=News&file=article&sid='.$fsid.'">'.$ftitle.' </a>';
}
at the end of this file
bevor the last brace "
}" (line ~55).